Multiplying apparatus



Feb, l5, 1949. A. c. HARDY ET AL MULTIPLYNG APPARATUS Original Filed July 8, 1944 SEE l JNVENTORS l AMEV.. c #M0949 ZW.. mp um a vvwkK $55k@ d v M y W v I l w. EM n u m wm :l||||}| -||l v l A H. L mm .i Y

Patented Feb. 15, 1949 arias MULTiPLYING APPARATUS Arthur Cil-Emily,`Wellesley,"Mass., and EdWard'C.

Dench, West Hartford, Conn.; assignorsto nyterchemical Corporation, New'York, N. Y.,`a

corporation of Ohio Original application July 8, 1944, Serial No. 543,990. Divided and this application December 3, 1946, Serial'No. 713,658`

This invention relates to multiplying apparatus.

This application isa division of our application "Serial No. 543,990, led July'8, 1944.`

The multiplication is effected on the basis of the probability principlethat, ifV an event a happens a% of the-time and an event b happens b% of the time, then theproportion of the time when 'bothevents occur is the product `of 1%. 13%. To utilize this principle, a series of rectangular waves (or square waves termed) is generated for each factor to be multiplied. In each series, the length of the pulses is so related to the length of the spaces between the pulses that the length of a pulse divided by the'length of a cycle (thatis, the effective length of the pulse) isequal to the iactor. In order to approach a random distribution'whichwoul'd resultin perfectly accurate multiplicationthe frequencies of the waves for each factor must be irrationally related. The frequencies should be so selected that, when the signals are combined, all beats are of suciently high frequency to be ltered out orare of small amplitude compared withthe amplitude of the wavesrepresenting the factors. The'multiplication iseffec'ted by leading'the series of square waves representing the factors to be multiplied to a collector which'indicates the percentage of the time during which pulsesoccur simultaneously in all the series.

:In .carrying out the inventioneach of a numberliof signals "representing factors to be multiplied is led toa square-wave generator. The generators'produce*series oi square waves of'diiferentfrequencies. Each generator isso contnolledby the signal which it receives that lthe ratio between the pulse :length and the cycle length in the series of Asquare waves which it generates is equal to the Areceived signal. The outputs o'f the lgenerators are, therefore, lseries of square waves representing the factors to be multiplied.

.The series of square waves corresponding to the `factors are led to a Acollector which `produces a signal which is equal to the proportion oilthe time .in which pulses occur simultaneously in all of the series and, therefore, proportional to the product of the factors.

The details of the electrical apparatus forming the'multiplier which has been described -may be greatly Varied within the scope .of our invention, but, for the sake of illustration, we will describe the particular apparatus and circuits which we have found most satisfactory. In .this description, we will referto the accompanyingk drawings in which:

as they are commonly A,

l Fig. 1 is a circuit diagram of an Ascmareewave generator; j and Fig. 2 is a4 circuit diagram of anvillustrative collector.

For thesake of illustration, we will describe apparatusfor computing the product inwhich c, m, and (1f-y) are factors'whichimay be'variables and Xcm is a constant coemcient.

Electric signals, ior example voltages, correspending to each of the quantitiesc, m and y are led to square-wave generators ,oi the type shown in Fig. 1. The upper part lof thisgure is a circult diagram and the lower part of the ligure snows the form of the waves and the potential to ground at different stages of the circuit.

Stage 2^ is a conventional triangular-wave generator and .stage 3 isan oscillator trigger circuit which, when triggered, generates a wave of much higher frequency than that of the triangular wave generated in stage 2.

The triangular wave Voltage from stage 2 and the signal voltage c from stage I are added and illustrative applied to the trigger circuit of stage 3. When Y the sum of the triangular wave Voltage and the signal voltage exceedsthe critical trigger voltage, theoscillator :of stage 3 is triggered and continues to oscillate until the signal voltage plus the triangular waVe voltage falls below this critical trigger Value. The per cent of time that the oscillator ison is proportional to thesignal Voltage. As a result, the oscillator produces groups of short waves separated by spaces as indicated in the diagram below stages 2 and 3 of the circuit. 'lhe frequency of the groups of short waves is the frequency of the triangular wavegenerated in stage 2,k while the ratio of the length of each group of waves to the length of the cycle, which, for convenience, we term the effective length of the group, is equal to the signal voltage c.

The groups of oscillationsfrom stage'3 are fed into stage t which is a detector `which-converts them into pulsesof D. C. constituting a conventional square wave. These square-wave pulses are sent to a poweramplifier which is stage 5 of thecircuit. When-the output of stage t is applied to thegrid ofthe power amplifier ci stage 5,--the residual ripple occurs below thecut-ofl grid Voltage and hence'does not appear in the output of stage 5 (see wave form shown below stages 4 and 5).

vThe output of stage 5 is a train of square Waves in which the effective length of the positive irnpulses corresponds to the signal which is fed to stage 2. This output may also be fed to an inverter forming stage 5 of the circuit. The output of the inverter is a train of squarewaves in which the effective length of the positive impulses corresponds to one minus' the signal'which is 'fed to stage 2.

The arrows along the bottoms of the different stages of the circuits shown in Fig` lindicate connections to D. C. potentials. The biases to be used are indicated by the diagram ,at the `bottom of Fig. l which shows the voltage relation between each stage and ground.

Fig. 2 shows a square-Wave collector. It receiVes trains of square waves representing the values c, m and (1y). The square Wave signals* representing c and m may be taken from stage 5 of the square-wave generators like that shown in Fig. l, to which voltages representing the values c and m are fed.l The square-wave signal representing the Value (l-y) may be taken from stage 6 of a square-"wave`v generator like that shown -in Fig. 1, to which a'voltage representing the value y is fed.

' Atthe left-hand side of Fig. 2 are shown leads from the square-Wave generators and inverters producing square-"Wavesignals representing the `values c, m, (1 -y). These three leads are connected together and to'the control grid of a multi-grid tube to produce a negative bias such that it cuts off the flow of plate current except whenipositive voltage pulses occur in all three Yconnected leads simultaneously. `Whenever this happens, the bias becomes sufoiently positive to permit the fiow of'plate'current in the multi-grid tube. The amplitude of the current pulses thus produced in the plate current of the multi-grid tube is controlled by the bias of the screen grid of the tube which is set by means of a potentiometer so that the amplitude of the plate current is proportional to the constant Xcm. The average plate current represents the product of the vamplitude of the current pulses and the fraction of the time when such pulses exist. It is, therefore, proportional tothe product cm (1-y) Xm To obtain a signal proportional to the average plate current,V the plate of the tube is connected 'to an R-C filter whose time constant is large enough to lter out the frequencies of the trains of square waves and beat frequencies so as to produce a D. C. voltage proportional to the average plate current. The time constant of the filter is, however, small enough to allow changes rapid enough to give adequate resolution at the speed of calculating used.

The plate current of the tube is passed through a load resistor L connected to the filter. The signal output voltage of the filter WiILtherefore, be proportional to the average plate current and will, therefore, be the required product.

What is claimed is:

1. Computing apparatus for obtaining the product of a number of factors, comprising means for generating a number of series of rectangular Waves at irrationally related frequencies and making the effective lengths of the impulses in each series correspond to one of the factors to be multiplied, and means for measuring the percentage of time during which impulses occur simultaneously in all said series.

2. Computing apparatus for obtaining the product of a number of factors, comprising means for generating a number of series of rectangular Waves at different frequencies and making the V and filtering out high-frequency beats.

3. Computing apparatus for obtaining the product of a number of factors, comprising means for generating a number of series of rectangular Waves at'diiferent frequencies and making the effective lengths of the impulses in each seriesv correspond yto one of the factors to be multiplied, leading saidseries to a common col- -lector which responds when impulses occur simultaneouslyl in all said series, and filtering the output of the collector.

A `4. Electrical means for computing the product of a number of factors, comprising a threeyelement electronictube, allow-pass filter connected in the'plate circuit of the tube, means for biasing thegrid of the tube sufficiently to cutoff the fiow of plate current, means for generating a number of series of rectangular voltage waves of different frequencies in each of which series the effective length of the positive impulses represents `on'e of the factors` to be multiplied, means for feeding said series of volt-v age waves Vto the grid of the tube, the intensity of the voltage impulses in the series being suifif cient to counterbalance the cut-off bias and to permit the flow of plate current when impulses occur simultaneously in all the series and insufcient to counterbalance the cut-off bias when impulses occur in less than all the series.

5. Electrical means for computing the product of a number of variable factors and a fixed factor, comprising an -electronic tube having two grid elemen'ts, means for biasing one of the grids ofthe tube sufficiently to cut off the flow of plate current, means for generating a number of series of rectangular voltage waves of different frequencies in each of which series the effective length of the positive impulses represents one of the variable factors to be multiplied, means for feeding said series of voltage waves `to the grid bias in opposition thereto, the intensity of the Voltage impulses in the series being sufficient to counterbalance vthe cut-off bias vand permit the fiow of plate current only when impulses occur simultaneously in all the series, and means for regulating the voltage of the other grid in proportion to the fixed factor so that the average plate current is proportional to the product of the variable and fixed factors.

6. Computing apparatus for obtaining the product of a number of factors, comprising generators for producing a number of series of rectangular waves of different frequencies and making the effective( length of impulses of the same polarity in each series correspond to one of the factors to bev multiplied, and a common collector connected to the generators to measure the percentage of time during which such impulses occur simultaneously in all the series.

7. Computing apparatus for obtaining the product of a number of factors, comprising generators for producing a number of series of rectangular Waves of different frequencies and making the effective length of impulses of the same polarity in each series correspond to one of the factors to be multiplied, a common co1- lector connected tothe generators and adapted to respond when such impulses occur simultaneously in all said series, and means for measurlng the average response of the collector.-

8. Electrical means for computing the product of a number of factors, comprising an electronic tube having a control grid, generators for producing a number of series of rectangular voltage waves of different frequencies in each of which series the eiective length of the positive impulses represents one of the factors to be multiplied, circuits for feeding all said series of voltage Waves to the control grid Iof the tube, the yvoltage level of the impulses in the several series being such as to produce on the grid a voltage which permits the ilow of plate current when positive impulses occur simultaneously in all the series and to produce on the grid a cut-01T bias when positive impulses occur in less than all the series.

9. Electricalmeans for computing the product of al number of variable factors and a iixed factor, comprising an electronic tube having two grid elements, generators for producing a number of series of rectangular voltage Waves 0f diierent frequencies in each of which series the eiective length of the positive impulses represents one of the variable factors to be multiplied, conductors connecting each generator with one of the grids of the tube, the voltage levels of the impulses of the Wave series being such as to bias the grid below cut-oil except when positive impulses occur simultaneously in all the series, and means for applying a voltage proportional to the xed factor to the other grid of 6 the tube, so that the average plate voltage of the tube is proportional to the product of the variable and xed factors.

l0. Electrical means for computing the product oi a number of factors, comprising an electronic tube having a control grid, generators for producing a number of series of rectangular voltage waves of different frequencies in each of which series the elective length of the positive impulses is proportional lto one of the factors to be multiplied, a circuit connecting said generators to provide a control voltage equal to a fixed proportion of the sum of the voltage in said series and to apply said control voltage to the grid of the tube, the operation of the tube being such that current flows in its plate circuit when the voltage applied to its grid is more positive than a value equal to said xed proportion of the sum of the positive impulses in one less than all said series.

ARTHUR C. HARDY.

EDWARD C. DENCH.

REFERENCES CITED The following references are of record in the ille of this patent:

UNITED STATES PATENTS Number Name Date 2,381,826 Levy-Savoye Aug. 7, 1945 2,401,779 Swartzel June 11, 1946 

